It seems strange in the context to say that coffee and pulla without the indefinite article is wrong. I understand that if you refer to an indeterminate amount of a food of drink in Finnish, you'd use the partitive, but English doesn't make the same distinction, so it seems strange to force it. Also, I think that "thanks" or "thank you" should be accepted for "kiitos", partly because that's what it means, but mostly because even though in this case it's standing in for "please", saying "thanks" in acceptance of an offer is not uncommon in English. (Arguably that last point is more applicable to the Q&A "- Kahvi? - Kyllä, kiitos" than to this one)
The Finnish mini dialogue "-Kahviko? -Ja pulla, kiitos" is something that could only happen in a service situation. It would not take place between friends where a "thank you" would be said because someone is offering you something. But when you buy, you would say "please", wouldn't you? In such a service situation in a cafe, for example, I think it would also be more common to ask if he customer wants "a coffee" rather than just "coffee". Although, as the English speakers are usually more talkative they would say even more than that.
In each of the exams you give, yes... Those are buns or individual serving style pastries. When I think of generic "pulla" though, I don't think of a "bun" at all. It's a bit like insisting that coffee cake, banana bread and a slice of lemon loaf should also be called a "bun". Obviously, this is early in the tree and Duolingo isn't intended as an exhaustive learning tool for foodies, but if someone was learning English and encountered the food item "bar-b-que", it would be like insisting that bar-b-que was a sausage and wondering why makkara wasn't accepted.
If you want to offer you guests coffee, you could say for example "Ottaisitko kahvia?" or "Ottaisitteko kahvia?" (latter one if more than 1 person).
"Kahviko?" is more like a confirmation where someone has already expressed that they want to drink "A coffee". Maybe a kiosk has "kahvi" on sale and you ask "Yksi kahvi, kiitos" (One coffee please).
It cannot be just "Coffee?" because that one would be "Kahviako" where someone has expressed that they want to drink an undefined amount of coffee "Haluan juoda kahvia" and you want to confirm it.
Apologies if this ended up being really messy, I'm a native speaker but my knowledge of linguistic terms is limited.
While it may be common to say thank you in this context, the formal use (kiitos vs. kiiti) here does imply the more formal "please". Knowing of course that "kiitos" is used in both cases (please/thank you), both answers should be accepted, but I also see this as a case of casual versus more formal register in the translation.
The English (neither UK, Aussie, Canada, nor USA) have licorice infused with ammonia chloride either. As such, if one was asking for "salmiakki", the English sentence would ALSO need to use the word "salmiakki". Do you throw a temper tantrum when confronted with crêpes, hollandaise sauce, lox, enchiladas, tacos, crème brûlée, souvlaki, gyros, schnitzel or borscht on a menu? You are (perhaps) more familiar with them, so it doesn't seem strange to you. When you learn a language divorced from the culture of its people, you are wasting your time. There is no such thing as "pulla" in English because it is unique to Finland. Would you rather type out "Finnish style, braided, yeast risen sweet bread flavored with cardamom and topped with pearl sugar" every time you are asked to translate pulla? If so, I have no further advice for you.
Onnea. Luulen, että tarvitset sitä...
If I make a pastry or sweet bread (a "bun") and flavor it with cinnamon, chocolate, lemon, raisins, or cherries, it won't be a "pulla". In Swedish, you can use the generic "bulle", but when you order, you might ask for a kanelbullar or a kardemummabullar. (not to mention the various lussebullar, fastlagsbullar, sommarbullar or even semlor...) Meanwhile in Finland korvapuusti, voisilmäpulla, laskiaispulla... It's ALL some form of cardamom bread. There are plenty of other sorts of pastries or breads, but none seem (at least in my research) to exclude the cardamom and still be called "pulla". Happy to learn otherwise though.